Dickens chose names for obvious and somewhat less obvious symbolism. In this way, a character’s name could characterize the character, and convey something important about the character.
Twist is a name given to Oliver when he is born, not his real name. Throughout the story, Oliver is constantly “twisted” around, as he is used by everyone he comes in contact with. Each of the other characters you mention use him.
Sowerberry of course makes one think of a “sour berry.” A berry is expected to be a good thing, and in fact Oliver is somewhat better off working as an undertaker’s assistant than in the workhouse. Soweberry is described with "features were not naturally intended to wear a smiling aspect, but he was in general rather given to professional jocosity" (enotes etext p. 16)
Indeed, he laughs at the idea of the poor dying and needing coffins. He is a bitter man. He notes that Oliver has a look of melancholy that would work for children’s funerals. ...
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